PRESUPPOSITIONS AND QUANTIFIER DOMAINS

Transcription

1 FRIEDERIKE MOLTMANN PRESUPPOSITIONS AND QUANTIFIER DOMAINS ABSTRACT. In this paper, I will argue for a new account of presuppositions which is based on double indexing as well as minimal representational contexts providing antecedent material for anaphoric presuppositions, rather than notions of context defined in terms of the interlocutors pragmatic presuppositions or the information accumulated from the preceding discourse. This account applies in particular to new phenomena concerning the presupposition of quantifier domains. But it is also intended to be an account of presuppositions in general. The account differs from the Satisfaction Theory and the Binding Theory of presuppositions in that it can be viewed as a conservative extension of traditional static semantics and in that it does not involve the notion of pragmatic presupposition. 1. INTRODUCTION To explain the behavior of presuppositions in complex sentences, sentences with connectives, modals, and attitude verbs has been a major challenge in more recent semantic theory and has motivated at least in part, the development of dynamic semantic theories, that is, roughly, theories that replace the traditional notion of a proposition as the meaning of sentences by that of a context change potential (a function from information states to information states). In this paper, I will give an outline of a conceptually quite different account of presuppositions. This account is based on a static semantics using structured propositions, double indexing, and certain kinds of minimal representational contexts as part of the content of an utterance. The central idea of the account can be illustrated by the behavior of presuppositions in attitude and modal contexts, as in (1a) and (1b): (1) a. John might read War and Peace, and he might finish reading War and Peace. b. John might finish reading War and Peace. (1a) does not itself presuppose what the sentence embedded under the second occurrence of might presupposes, namely that John was Synthese (2006) 149: Ó Springer 2006 DOI /s y

2 180 F. MOLTMANN reading War and Peace before. It suffices that he did so in the relevant possible worlds. By contrast, (1b) does presuppose that, namely that John was reading War and Peace before. The difference between (1a) and (1b) obviously is that in (1a) what is presupposed is explicitly mentioned in the preceding modal sentence, whereas in (1b) it isn t. In the terms I will use, this means that lexical presuppositions (such as the one of finish) must either be anaphorically linked to an antecedent (which is part of the representational context that I will make use of) or else be evaluated as true with respect to the context of the utterance (rather than the current index). The central idea of my account is that this apparently disjunctive condition is a manifestation of a single fundamental requirement on presuppositions, namely that presuppositions be semantically anchored, which means that presuppositions must be verified prior to the evaluation of the expression triggering the presupposition at the current index, in the course of the evaluation of the truth value of the sentence. The account is in particular designed to deal with a novel kind of presupposition that involves the domain of strong quantifiers (e.g. every, the, most) and displays the semantic anchoring condition in quite analogous ways, as in (2a,b): (2) a. John might write ten books, and he might publish every book. b. John might publish every book. Whereas the domain of every book in (2a) can be identified with the set of (possible) entities introduced by ten books, in (2b) it must consist of the actual entities identified by the utterance context. That is, in (2a) the domain of every book is anaphorically linked to some preceding descriptive content, whereas in (2b) it is identical to the domain the quantifier would have relative to the context of the utterance. What is presupposed in the case of strong quantifiers is a set of objects rather than a proposition. Thus, in this case, semantic anchoring will require the prior identification of a domain, rather than the prior verification of a proposition, in relation to the evaluation of the presupposition trigger. Empirically, this Domain Presupposition manifests itself foremost in intensional contexts. But also the restriction of there-sentences to weak quantifiers (e.g. no, few, several) can be analysed in its terms. Moreover, the two ways of satisfying the anchoring condition of domain presuppositions provide a natural explanation of the apparent ambiguity between anaphoric and Russellian uses of definite descriptions.

3 PRESUPPOSITIONS AND QUANTIFIER DOMAINS 181 On the dynamic semantic view, presuppositions are preconditions to be met by an information state in order for a presupposition-carrying sentence to be applicable to that state. The present account makes no use of contexts defined in terms of pragmatic presuppositions which are central on any dynamic account. In fact presuppositions are accounted for mainly within nonintentional terms, making use only of the course of the truthconditional evaluation of a structured proposition together with a supplementing minimal representational context. The account has features in common, though, with the one developed within Discourse Representation Theory (DRT), the Binding Theory of presuppositions developed by van der Sandt and Geurts. Unlike the latter, the present account is based on fundamentally different semantic notions, though, such as static meanings of sentences and double indexing and the notion of propositional content, construed as a structured proposition. The present account differs from the Binding Theory also in a number of other conceptual and empirical respects, concerning the status of global accommodation, the distinction between anaphoric and nonanaphoric presupposition triggers, and cases of local accommodation. It is an important insight of the dynamic semantic approach that the previous discourse may play an important role for the meaning of a sentence. 1 However, rather than taking this to require a radical reconception of the notion of sentence meaning, the present account uses a notion of a discourse-driven context in a minimal way: as supplementing a traditional notion of propositional content and as being driven entirely by anaphoric relationships involving expressions of the sentence in question. The first part of the paper gives an outline of my account of presuppositions of propositions, using some rather standard conception of structured propositions. It starts with an exposition of the semantic dynamic account of presupposition projection, that is, the Satisfaction Theory. Then two major problems for this account, which have lead to the development of the Binding Theory within DRT, will be addressed and accounted for within what can be considered a conservative extension of traditional double-indexing semantics. The second part of the paper extends the account to presupposition of quantifier domains, treating familiar and new phenomena involving the distinction between weak and strong quantifiers.

4 182 F. MOLTMANN 2.1. The Central Idea 2. PRESUPPOSITIONS The central idea about presuppositions in complex sentences that I will explore is as follows. Presuppositions are conditions that need to be verified, at least in part, prior in the procedure of evaluating the truth value of a sentence than the semantic evaluation of the presupposition trigger. This requirement of semantic anchoring of presuppositions can be satisfied in one of two distinct ways: either the presupposition is verified with respect to the utterance context (in addition to the index) or else it corresponds to explicit material which has already been evaluated semantically and acts as an antecedent of the presupposition trigger. These two disjunctive ways are manifested by conceptual presuppositions carried by lexical items such as finish and repeat as well as the domain presupposition of strong quantifiers such as every and most. Some expressions are limited to the second way of satisfying the anchoring condition, though, namely expressions like again and too, or the quantifier each. Others, namely sortal requirements, are limited to the first way Propositions as Structured Propositions A fundamental feature of my account is that it maintains a traditional notion of propositional content. In fact, it uses a conception of propositional content as a structured proposition, certainly the most widely accepted notion of proposition in the philosophy of language, especially for construing the object of propositional attitudes (cf. Cresswell 1985; Soames 1987). 2 Structured propositions also have particular advantages for the treatment of presuppositions. First, structured propositions are particularly suitable for construing the relevant notion of a discoursedriven context. On the account I propose, the evaluation of a sentence will be made dependent on a discourse-driven context (a background ), but this context will be limited to representing information that is required by anaphoric elements in the sentence. The material in such a context will be mentally activated, structured elements, either structured propositions or properties. If the propositional content is itself a structured proposition, it will be of the same nature as those background elements. With a structured propositions conception of context and content, also anaphoric

5 PRESUPPOSITIONS AND QUANTIFIER DOMAINS 183 relations between constituents of the proposition and elements in the background can be straightforwardly established. 3, 4 At this point I will present one version of a structured propositions account, namely basically that of Soames (1987), but only for structured propositions for sentences without presuppositions. Later the account will be modified for the purpose of presuppositions. While a sentence like (3a) may be taken to express the proposition that is a pair consisting of a property and two objects as in (3b), a quantificational sentence like (4a) will express a proposition consisting of a quantifier and a predicate, as in (4b), with the quantifier being, at a world w, the set of sets defined in (4c): (3) a. John likes Mary. b. LIKE, j, m> (4) a. Everybody left. b. <EVERY(PERSON), LEAVE> c. X 2 EVERY(PERSON) w iff PERSON w X. Here LIKE is a two-place property and LEAVE a one-place property, each of which having an extension at a given world. Structured propositions will themselves be truthconditionally evaluated as in (5a) and (5b) for (3a) and (4a): (5) a. [<LIKE, j, m>] w ¼1 iff <j, m> 2 LIKE w. b. [EVERY(PERSON), LEAVE>] w ¼1iff LEAVE w 2 EVERYBODY w. Similarly, complex sentences with conjunctions and conditionals will express structured propositions as in (6) and (7) (tense being neglected), with the truth conditions given there (cf. Soames 1987): (6) a. John came and Mary left. b. [AND, COME, j>, <LEAVE, m>>] w ¼1iff < [<COME, j>] w, [<LEAVE, m>] w >2 AND w (7) a. If John comes, Mary leaves. b. [<IF, <COME, j>, <LEAVE, m>>] w ¼1iff <[<COME, j>] w, [<LEAVE, m>] w >2 IF w AND has as its extension at any world the relation that holds between two truth values just in case they are both true; IF, viewed as material implication, has as its extension at any world the relation that holds between truth values t and t 0 just in case t is false or t 0 is true.

6 184 F. MOLTMANN Sentence with indefinites and/or unbound anaphora ( donkey - anaphora) will express structured propositions with variable-like objects ( discourse referents ), that is, objects whose primary function is to be replaced by real objects in the evaluation of the truth value of a sentence. I will call these objects parametric objects, following a closely related notion used in Situation Semantics (Gawron and Peters 1990). Thus, a donkey-sentence like (8a) will express the complex structured proposition in (8b) containing the parametric object x 1, which will be evaluated by quantifying over anchoring functions, based on the evaluation of simpler structured propositions as in (8c): (8) a. If John buys a book, he reads it. b. [<IF, <<BUY, j, x 1 >, <BOOK, x 1 >>, <READ, j, x 1 >>] w, f ¼1 iff for all objects d and anchoring functions f 0 that differ from f in assigning d to x 1, [<IF, <<BUY, j, x 1 >, <BOOK, x 1 >>, <READ, j, x 1 >Š w;f 0 ¼1. c. [<<BUY, j, x 1 >, <BOOK, x 1 >>Š w;f 0 ¼1 iff <j, f 0 (x 1 )> 2 BUY w;f 0 and f 0 (x 1 ) 2 BOOK w;f 0 This treatment of donkey-sentences is a fairly standard one, simply cast within a structured-propositions approach and thus requiring parametric objects as constituents of propositions. It is introduced here because it will later on be made use of. In what follows I will use the function st as a mapping of expressions of English, relative to an (utterance) context, to meanings that is, structured propositions or possible constituents of structured propositions. Thus, sst w is the structured proposition expressed by S at the context w and (sst w ) w0 the truth value of S at w 0. snt w is the property expressed by N at w and (snt w ) w0 is the extension of N at w Views of presuppositions I will start with some important notions and distinctions that will play a role in this paper. First, there are two conceptually rather distinct notions of presupposition: semantic presupposition and pragmatic presupposition. Semantic presuppositions are relations between linguistic units (sentences, utterances, or propositions), whereas pragmatic presuppositions are the contents of a kind of propositional attitude, namely that of taking something for granted in the context of conversation. Whereas the former notion has had a

7 PRESUPPOSITIONS AND QUANTIFIER DOMAINS 185 long tradition in the philosophy of language and linguistic semantics, the latter notion has been established as such mainly in the work of Stalnaker (1970, 1973, 1979). In dynamic semantics, the two notions have been closely linked, and this sometimes has led to a disregard of the original conceptual distinction. A central distinction in this paper is that between context and index (cf. Kamp 1971; Kaplan 1977; Stalnaker 1979; Lewis 1981). Context is the context of utterance (consisting at least of the world and the time at which the utterance is made), whereas the index is an additional circumstance that may diverge from the first one as a result of evaluating an intensional operator (consisting of the world and perhaps time of evaluation). Relative to a context a sentence has a content, or expresses a proposition, and relative to a context and an index it has a truth value. An index and especially a context may consist in more than a world, but I will generally disregard other possible parameters. There are two traditional notions of semantic presupposition: the Fregean notion of presuppositions as preconditions for the truth or falsity of a sentence (logical presupposition) and the Strawsonian notion of presupposition as a precondition for a sentence to express a proposition (expressive presuppositions) (cf. Soames 1989). Following Soames (1989), this distinction can be construed in terms of double indexing as follows. Expressive presuppositions need to be fulfilled by the context in order for a sentence to have a content, whereas logical presuppositions need to be fulfilled in order for a sentence to be either true or false at an index (that is, a world of evaluation). Expressive presuppositions generally are referential presuppositions imposed by singular terms, whereas logical presuppositions come about in various ways either on the basis of lexical meanings (preconditions for the applicability of concepts) or on the basis of syntactic constructions (e.g. clefts). In what follows, I will deviate from Soames s suggestion in taking also conceptual presuppositions to sometimes act as conditions on a context and thus as preconditions for a sentence to have a content. In the development of dynamic semantics, a close link has been posited between semantic presuppositions and pragmatic presuppositions, that is, propositions taken for granted in the context of conversation: Semantic presuppositions must be pragmatically presupposed for a sentence to be acceptable in a context of conversation, and the notion of pragmatic presupposition has been taken to be crucial for explaining how presuppositions of component

8 186 F. MOLTMANN sentences are inherited by complex sentences, especially the familiar facts illustrated in (9) (cf. Stalnaker 1979; Heim 1983): (9) a. John asked a question and then repeated the question. b. If John has asked a question, he will repeat the question. c. John repeated the question. d. John did not repeat the question. Only (9c) and (9d), but not (9a) or (9b) presuppose that John asked the question before. Whether a complex sentence inherits a semantic presupposition from a component sentence depends, so the view, on changes in pragmatic presupposition in the course of the acceptance or processing of the complex sentence in a conversation. This is the basic idea of the so-called Satisfaction Theory of presuppositions (Karttunen 1974; Heim 1983, and subsequent work). The Satisfaction Theory makes crucial use of the notion of common ground or context set, the set of worlds compatible with what is pragmatically presupposed in the context of conversation (cf. Stalnaker 1970, 1973, 1979). One fundamental idea of the Satisfaction Theory is that the semantic presuppositions of a simple sentence need to be entailed by the context set relative to which the sentence is uttered. The other fundamental idea is that the meaning of (at least certain) connectives, in particular conjunction and the conditional, involves a change in the context set from the initial or global context to another, local context. The Satisfaction Theory requires semantic presuppositions of component sentences to be entailed only by the relevant local context not the global (or initial) context (Heim 1983; cf. Stalnaker 1979; Karttunen 1974; among others). This applies to a conjunction S and S 0 as in (9a) as follows: S is applied to a global context c first; so the presuppositions of S need to be entailed by c. Then a new context c 0 arises from adding the information of S to c, a context to which S 0 applies, requiring that the presuppositions of S 0 be entailed by c 0. When a sentence if S, then S 0 as in (9b) applies to a context c, then S is applied to c first, that is, the presuppositions of S need to be entailed by c. Then the information given by S can be added to c yielding a context c 0 to which S 0 will then apply, requiring its presuppositions to be entailed by c 0. More formally, the dynamic semantics of simple sentences and sentences with negation, conjunction, and the conditional are as follows, where S<p>is a simple sentence presupposing p:

9 PRESUPPOSITIONS AND QUANTIFIER DOMAINS 187 (10) a. c[s<p>]¼{w w 2 c & S is true in w}, if c entails p; undefined otherwise. b. c[:s]¼c\c[s] c. c[s & S 0 ]¼c[S][S 0 ] d. c[s! S 0 ]¼c\(c[S]\c[S][S 0 ]) If S is the first conjunct of a conjunction or the antecedent of a conditional, the processing of S will change a global context c to a local context c 0 which differs from c in containing the information given by S. In both cases, any presupposition of the second conjunct or consequent S 0 will be inherited by the entire sentence just in case the presupposition is not expressed or implied by S. The Satisfaction Theory locates the satisfaction of presuppositions at the level of the index, rather than the context: the context set is in fact nothing but the set of indices at which the previous discourse is true. We will see that locating presupposition satisfaction at the index is one source for the inadequacy of the Satisfaction Theory. 3. PROBLEMS FOR THE SATISFACTION THEORY The Satisfaction Theory is quite appealing for sentences with connectives and quantifiers. However, it has difficulties with complex sentences involving an intensional operator (cf. Geurts 1995, 1996, 1998). In order for the Satisfaction Theory to apply to sentences embedded under modal or attitude verbs, it needs to draw a distinction between two sorts of contexts: primary contexts, representing the speaker s presuppositions about the world, and secondary contexts, representing what is presupposed about the content of the relevant modality or the relevant agent s propositional attitude (cf. Stalnaker 1987; Geurts 1995, 1998). 5 This will account for examples like (11a) where the presupposition of he continues going to school need not be satisfied in the actual world, but will be satisfied with respect to the set of worlds in which the previous piece of discourse information John goes to school is true. (11) a. John must go to school, and he must continue going to school. The problem is that without such a previous piece of information, the presupposition must be satisfied in the actual world: (11) b. John must continue going to school.

10 188 F. MOLTMANN (11b) presupposes that John actually goes to school, not only that he is required to do so. (11b) constitutes a major problem for the Satisfaction Theory: the Satisfaction Theory predicts that (11a) only presupposes (or rather requires accommodation of the presupposition) that John is required to go to school, not that he in fact goes to school. That is, it predicts that the context that will be modified so as to include the information that John goes to school is the secondary, not the primary context. In other words, the Satisfaction Theory predicts local, not global accommodation (cf. Geurts 1998). The generalization about presuppositions in modal and attitudinal contexts that has been established is as follows: The presuppositions of a presupposition trigger in the scope of an intensional operator are always inherited by the entire sentence, unless there is preceding linguistic material in the same intensional context that matches the presupposition (cf. Geurts 1995). That this also holds for attitude verbs is seen in (12) (cf. Karttunen 1974; Heim 1992; Geurts 1995, 1998): (12) a. Mary believes that John repeated the question. b. Mary believes that John asked the question before, and she believes that he repeated the question. (12a) (for most speakers) presupposes that John asked the question, whereas (12b) does not. Again, the Satisfaction Theory wrongly predicts that what will be accommodated in this case is the secondary context, not the primary one. Let me call the phenomenon displayed by (11a, b) and (12a, b) the de re effect. Another general problem for the Satisfaction Theory is what Geurts calls the proviso problem (cf. Geurts 1986). In many cases, it appears, the Satisfaction Theory predicts weaker presuppositions than a complex sentence actually carries. For example, the Satisfaction Theory predicts that (13a) only presupposes (13b): (13) a. It is possible that Theo hates sonnets and that his wife does too. b. Theo hates sonnets! Theo has a wife. If contexts are construed as sets of possible worlds, then once the sentence Theo hates sonnets is applied to a context, the resulting context also supports all of that sentence s implications and thus it

11 PRESUPPOSITIONS AND QUANTIFIER DOMAINS 189 is sufficient that Theo has a wife is among those. However, (13a) in fact presupposes unconditionally that Theo has a wife. 4. THE BINDING THEORY OF PRESUPPOSITIONS Within DRT (Kamp 1981; Kamp and Reyle 1996), Rob van der Sandt and Bart Geurts have developed an alternative to the Satisfaction Theory, the Binding Theory of presuppositions (van der Sandt 1992; Geurts 1995, 1996, 1998). Only a few remarks about this approach should suffice, for readers already familiar with DRT. According to the Binding Theory, presupposition triggers are always anaphoric, requiring an antecedent in an accessible discourse representation structure (DRS). Instead of taking presupposition satisfaction to go along with the stages of acceptance of information, the acceptability of presupposition triggers is now traced to a formal relation of accessibility. The Binding Theory always requires an explicit antecedent to be present in the DRS that will satisfy the presupposition, and in the absence of a linguistically explicit antecedent, accommodation has to take place, that is, the insertion of an antecedent into an accessible part of the DRS. The de re effect observed in (11a, b) and (12a, b) is accounted for by giving preference to global accommodation over local or intermediate accommodation that is, insertion of an antecedent into the highest level of the DRS. The Binding Theory of presuppositions faces several difficulties. First, the Binding Theory ultimately does not draw a difference between presuppositional and assertive elements. Once a presupposition is accommodated, especially globally, it is put on a par with the assertive elements in the sentence. The presupposition does not act anymore as a precondition for the truth or falsity of the sentence or as the content of a pragmatic presupposition. Second, in the case of global accommodation the Binding Theory fails to account for the fact that the presupposition also needs to be satisfied by the relevant secondary context. For example in (12a), Mary must also believe that John asked the question before (cf. Karttunen 1974; Stalnaker 1988; Zeevat 1992). Third, there are problems with the way local and intermediate accommodation are treated. One problem is that local or intermediate accommodation on the Binding Theory should always be possible when it is known that the presupposition is not true. However, this does not seem the case, Compare (14a) with (14b):

12 190 F. MOLTMANN (14) a. If John is married, his wife is happy. b. If John plays baseball, his wife is happy. (14a) is fine because the antecedent implies that John has a wife. But for (14b) a reading on which John does not have a wife seems excluded even if it is not known that John has a wife: local accommodation of his wife is impossible. Another problem with local and intermediate accommodation for the Binding Theory arises with quantificational sentences. The Binding Theory says that intermediate accommodation must take place with quantificational sentences like (15), that is, accommodation of a proposition x smoked within the restriction of the quantifier, making (15a) equivalent to (15b): (15) a. Two students stopped smoking. b. Two student who smoked stopped smoking. This, however, yields wrong predictions when such sentences are embedded under attitude verbs or modals, as in (15c, d): (15) c. It is possible that two student stopped smoking. d. John believes that two student stopped smoking. According to the Binding Theory, the presupposition will have to be accommodated within the scope of the modal or the attitude verb. But the de re effect is apparent in such sentences in just the same way as elsewhere. That is, (15c) and (15d) presuppose that two students in fact did smoke. There is another general problem for both the Satisfaction Theory and the Binding Theory, and that is that it neglects either one or the other kind of two fundamentally different sorts of presuppositions. Kripke (ms) (see also Soames 1989, Fn. 54) convincingly argued for a distinction among two different kinds of presuppositions: anaphoric presuppositions and nonanaphoric ones. Anaphoric presuppositions are those carried by expressions like too and again. Nonanaphoric presuppositions may be carried by lexical expressions like stop, which can also have a nonanaphoric reading (cf. Soames Fn. 54). Anaphoric presupposition triggers relate to a specific proposition in the context, usually one made explicit in the previous discourse context. Clearly, the Binding Theory is an account designed for anaphoric presuppositions, whereas the Satisfaction Theory is made for nonanaphoric ones. 6 Let us then distinguish between purely anaphoric presupposition triggers such as again on the one hand and on the other hand

13 PRESUPPOSITIONS AND QUANTIFIER DOMAINS 191 presupposition triggers such as stop, which have both anaphoric and nonanaphoric uses. The latter generally are expressions that have concepts as meanings that impose the presuppositions as preconditions for their applicability. For such conceptual presuppositions the following generalization can be made: Unless the presupposition is anaphoric, it must be satisfied with respect to the context (and not just the index). This captures the de re effect and it reduces the projection problem of presuppositions to the establishing of anaphoric presuppositional relations (as on the Binding Theory). To complete the picture, there may also be purely nonanaphoric presuppositions, as Rob van der Sandt pointed out to me, namely sortal requirements. Sortal requirements cannot have an anaphoric use, simply because they are conditions on the kind of argument a predicate can take that would, for a given object, need to hold in all possible worlds. 5. A NEW ACCOUNT OF PRESUPPOSITIONS My account carries over some important features of the Binding Theory, namely the anaphoric treatment of at least certain presuppositions, and with that the account of the proviso problem and, to an extent, the de re effect. However, my account makes a distinction between anaphoric and nonanaphoric presuppositions, which are treated in two fundamentally different ways. 7 Nonanaphoric presuppositions are conditions that need to be satisfied with respect to the utterance context. Anaphoric presuppositions are presuppositions acting as anaphora and as such need to link up to an antecedent. The antecedents of anaphoric presuppositions need to be found in a context that I call the background of a structured proposition. The background is a minimal representational context that provides the anaphoric completion for a sentence, and thus contains the kind of semantic material from the previous discourse context that can provide antecedents of certain anaphorically used expressions in the sentence. For sentences presupposing a proposition, the backgrounds consist of propositions acting as anaphoric completions for the relevant anaphorically used presupposition triggers. For example, the background for John failed again will have to contain a proposition of the sort that John failed previously. It is this proposition itself that I will take to act as the antecedent of the again-

14 192 F. MOLTMANN sentence. For an again-sentence to be acceptable, the again-sentence needs to be coindexed with such a proposition in the background. 8 We can then say that anaphoric presuppositions impose the following condition on what can count as a background, where S and p are variables ranging over both indexed and nonindexed sentences and propositions: (16) Condition on anaphoric presuppositions If a sentence S anaphorically presupposes a proposition p, then b can be a background for S only if S is coindexed with p and p 2 b. Here I am assuming that a simple sentence containing a presupposition trigger such as John failed again carries an index and not just the presupposition trigger itself. There will not always be a single background associated with the interpretation of a sentence. Rather backgrounds may change within the evaluation of a sentence, especially in the case of conditionals and conjunctions (just as they do in dynamic semantics). This change will involve an increase of information as goes along with the preceding subsentence. Even a sentence-internal change of the background is not strictly driven by the semantic content of subsentences, but may, to an extent, also depend on a speaker s intentions (which will account for rare cases of local accommodation). Let us say that a background b(c) depends on a context c, representing relevant speaker s intention as well as the preceding discourse. Then if b(c) is the background for a conjunction S and S 0, the background for S 0 will also depend on the content of S, and thus for the semantic evaluation of S 0 we will have a background b(c, S). Similarly for a conditional if S, then S 0. Thus, we will have the conditions on backgrounds of embedded sentences in (19a, b): (17) a. [S and S 0 ] i, b(c) ¼<AND, [S] i, b(c),,[s 0 ] i, b(c, S) > b. [if S then S 0 ] i, b(c) ¼<IF, [S] i, b(c),,[s 0 ] i, b(c, S) > For a sentence with an intensional verb V, the background for the embedded sentence generally contains propositions embedded in the same way in the background for the entire sentence, as in a simple case in (17c): (17) c. [a VS] i;f½vš;a;p>g ¼½VŠ; a; ½SŠ i;fpg > That is, the embedded sentence in John must continue going to school in (11a) will be evaluated as [John continues going to school] i;fg;j;s>g where fg; j; s > is the proposition expressed by John goes to school.

15 PRESUPPOSITIONS AND QUANTIFIER DOMAINS 193 I do not intend to give explicit rules for the construction of backgrounds. It suffices to say that those rules differ fundamentally from semantic rules determining the propositional content of a sentence: they do not apply strictly on the basis of the syntactosemantic structure of a discourse, but are also influenced by the speaker s intentions. The process of building backgrounds, in a way, is a partly dynamic process, of cumulatively building relevant antecedent material for anaphoric elements. This then incorporates a fundamental insight of dynamic semantics, namely that the interpretation of sentences may depend on a discourse context that is incrementally built even within a sentence. A background will form the content of the propositional attitude of pragmatic presupposition, or else, in the case of an embedded sentence, the content of a background attitude (usually belief). On this account then, pragmatic presuppositions will naturally go along with semantic anchoring, but do not play a direct role for presupposition projection. Conceptual presuppositions may be satisfied either with respect to the background or with respect to the utterance context. Thus, in (18a), John stopped smoking relates anaphorically to the proposition that John smoked from the antecedent of the conditional, whereas in (18b) the proposition needs to be true in the actual world, that is, with respect to the utterance context: (18) a. If John once smoked, then he now stopped smoking. b. If Mary is happy, then John stopped smoking. In the second case, as was mentioned in regard to the Binding Theory, the presupposition needs to be true also at the index. Turning now to the condition on conceptual presuppositions, let us recall that a sentence will first be evaluated as a structured proposition relative to an utterance context as well as a background. The structured propositions will then be the bearer of the truth value, relative to an index. I take the conditions on conceptual presuppositions to be conditions on whether a sentence expresses a structured proposition, relative to a context and a background, following Soames (1989) suggestion mentioned earlier. If a conceptual presupposition is satisfied anaphorically, the sentence needs to be coindexed with a corresponding proposition in the background, and if it is satisfied with respect to the utterance context, it needs to be true at that context. In both cases, the presupposition also needs to holds at the current index, though, and this effect can be achieved by making the presuppo-

16 194 F. MOLTMANN sition itself part of the structured proposition, as an additional conjunct. The condition on conceptual presuppositions will then be as follows: (19) Condition on conceptual presuppositions For a sentence S<p> presupposing a proposition p, [S<p>] i,b is defined as <[S] i,b, p> if either p i ¼1 or S is coindexed with p and p 2 b. An important question is, why should conceptual presuppositions be subject to a disjunctive condition of either being anaphoric with respect to elements from the previous discourse or require truth relative to the context of the utterance situation? There is a unifying motivation for this disjunctive condition, namely what I will call semantic anchoring: (20) Semantic anchoring of presuppositions If an expression E in a sentence S presupposes a proposition p, then p must have been verified prior to the evaluation of E at the current index. Prior here refers to the order of the various steps involved in the evaluation of the truth value of a sentence, which is not to be understood in temporal terms. (20) will be satisfied just when the presupposition p belongs to the background or has been verified with respect to the context. For a sentence S that is to be evaluated at a context i, an index i 0, and a background b, certainly whatever conditions associated with S need to be satisfied at the context i need to be verified prior to the evaluation of S at the index i; and the background b contains, by nature, already evaluated material. Semantic anchoring in a way unburdens the current index, from having itself to verify presuppositions. To explain presupposition projection of complex sentences, only the semantic anchoring condition is needed, together with the rules governing the construction of backgrounds for subsentences. With this general account of presuppositions, let us return to the problems noted for the Binding Theory and see how they can now be dealt with. First, the present account draws a clear distinction between presupposed and asserted elements in that presuppositions are either to be verified at the context or else must find an antecedent in the background. Second, the disjunctive condition in a way

17 PRESUPPOSITIONS AND QUANTIFIER DOMAINS 195 explains the preference for global accommodation, rather than stipulating it, in that verification with respect to the context is simply one way of satisfying semantic anchoring. Third, the problems with local and intermediate accommodation that the Binding Theory faces are well accounted for. Local accommodation is limited to cases where a background can be construed from more or less explicit information in a preceding sentence. On the present account instead of local accommodation, there will only be a process of extracting antecedent material from the information content of a preceding sentence, which can be effectively applied to (14a), but not (14b). Also no problem arises in cases such as (15c) and (15d). The anchoring condition says that for any student d the presupposition that d smoked before needs to be true at the utterance context, rather than just an index introduced by the modal, and it imposes that condition on every student The Basic Idea 6. THE DOMAIN PRESUPPOSITION The account of presuppositions that I have given has an important application to quantifier domains. Some quantifiers, namely strong quantifiers such as every, most, and the, display the same disjunctive condition concerning their domain as conceptual presuppositions. The presupposition of strong quantifiers, however, involves quantifier domains rather than propositions and hence can be called the Domain Presupposition. On the present account, this means that strong quantifiers have a restriction that is either coindexed with a property in the background or else must be evaluated with respect to the utterance context and not just the current index. Note that the domain presupposition is not the condition that the quantification domain of strong quantifiers be nonempty, as in Milsark (1977), Diesing (1991) and others. Rather the Domain Presupposition concerns the identification of the quantifier domain prior to the evaluation of the quantificational NP at the current index. The domain presupposition thus presents a novel kind of presupposition in that what is presupposed is not a proposition, but a domain. Indeed the fact that the domain presupposition involves as a presupposition a domain rather than a proposition is something difficult do deal with on most existing accounts of presuppositions, including the Satisfaction Theory (where a context is conceived as a set of possible worlds (and possibly variable assignments)). The exception of course is the

18 196 F. MOLTMANN Binding Theory where presuppositions are treated as anaphora, allowing in principle any semantic object to be presupposed. There is in fact an account of the domain presupposition within the Binding Theory, namely that of Geurts and van der Sandt (1999). The aim of their paper, however, is to account for the existence presupposition of strong determiners within the Binding Theory of Presuppositions in general, rather than exploring an alternative account of the presuppositions of strong determiners with its various empirical ramifications. 9 Their account moreover poses the same issues and difficulties as the Binding Theory of presuppositions of propositions, as we will see. The distinction between weak and strong NPs itself, I will argue, should be characterized in terms of the Domain Presupposition, which then allows for an explanation of their different occurrences. But the fact that definite NPs denote strong quantifiers and thus presuppose their domain has also other interesting consequences. In particular, the existence and uniqueness presuppositions associated with definite determiners will now come out as consequences of the Domain Presupposition and need not be specified as presuppositions anymore The Weak-strong Distinction Among Quantifiers Let me first present some fundamental properties of the weak strong distinction as such in order to introduce my account of the weak strong distinction in terms of the Domain Presupposition. I will adopt Keenan s (1987, 1996) logical characterization of strong quantifiers as those quantifiers that are nonintersective; but I will argue that it is not this characteristic that explains the different behavior of weak and strong quantifiers, but rather a property that goes along with nonintersectiveness, namely the Domain Presupposition. The most familiar and best-researched contexts in which the weak strong distinction among quantifiers plays a role are theresentences (discussed as the so-called (In)definiteness Effect )). Theresentences reject the NPs in (21) and accept those in (22): 10 (21) a. # There is every man/the man/john in the garden. b. # There are most men in the garden. c. # There are many/few men in the garden. ( many/few relative to the number of men )

19 PRESUPPOSITIONS AND QUANTIFIER DOMAINS 197 (22) a. There is/are a man/three men/a few men/many men/no men in the garden. b. There are less than two/more than three/exactly two men in the garden. The acceptability of certain complex NPs in there-sentences is also of interest, namely Boolean combinations of quantified NPs or partitives. I will turn to those later. There are two kinds of approaches to the characterization of NPs acceptable in there-sentences. The first proposal characterizes such NPs in terms of a logical property of their determiner (Barwise and Cooper 1979; Higginbotham 1987; Keenan 1987, 1996); the second in terms of a discourse-related property (Milsark 1974; Enç 1991; Diesing 1992). The present account is in a sense a combination of the two views. It takes the distinction to be based on logical properties, which in turn go along with context-related properties. But it takes the context-related properties, not the logical properties to be crucial for explaining the different behavior of weak and strong NPs. Moreover, even though in the case of simple NPs the context-related property goes along with the logical property, in the case of complex NPs the two properties do not always coincide. The relevant logical property is best formulated within Generalized Quantifier Theory (cf. Barwise and Cooper 1979). On the generalized-quantifier view, NPs denote generalized quantifiers Q (that is, sets of sets) and determiners denote functions D (which themselves are called determiners ) mapping a set A onto a set of sets B (or, equivalently, a function from sets B to truth values 1 or 0). For example, every will denote a function which maps a set A to a function mapping a set B to 1 iff A is included in B, and (singular) the will denote a function that maps a set A to a function mapping a set B to 1 if A is included in B and A is a singleton set, to 0 if A is not included in B and A is a singleton set, and to the third truth value # (Ôundefined ) otherwise. According to Keenan (1996), whom I will follow in this regard, the logical property of determiners of simple NPs acceptable in there-sentences is the property of denoting an intersective determiner, where a determiner is intersective just in case it only cares about the intersection of its two arguments (cf. Keenan 1996): 11 (23) A determiner D is intersective iff for all A, A 0,B,B 0,ifB2 D(A) and A \ B¼A 0 \ B 0, then B 0 2 D(A 0 ).

20 198 F. MOLTMANN In a derivative use, I will say that a determiner as an expression of English is intersective just in case it denotes an intersective determiner in the sense of (23). I will also say that an NP is intersective just in case its determiner is intersective. A as in a man is in the garden is intersective because it only cares about how many things are both men and in the garden; it need not take into account the entire set of men. But, every as in every man is in the garden is not intersective, since it has to check whether all the entities in the restriction, the set of men, are in the extension of the predicate, the set of things in the garden. 12 Nonintersective determiners, I want to argue, are precisely those determiners that presuppose their domain, which means that their domain needs to be semantically anchored in a way analogous to the semantic anchoring of conceptual presuppositions. That is, the domain of nonintersective determiners needs to be identified prior to the semantic evaluation of the determiner at the current index. In the case of presuppositions of propositions, those presuppositions were either specifically associated with anaphoric presupposition triggers or else they were preconditions on the application of a concept (and thus predictable given the nature of the concept). The question then arises of why strong quantifiers, but not weak quantifiers, should presuppose their domain. An answer to this question can be obtained from the property of nonintersectiveness: in order to verify whether a set belongs to a nonintersective quantifier, the entire domain of the quantifier must be identified; whereas to verify whether a set belongs to an intersective determiner, only a subset of the quantifier domain needs to be identified. If membership in the extension of a concept depends on the precise identity of another set, then there is a sense in which it depends on that set. Let us then say that the relation among a set of sets Q and a set A (or a set of properties and a property) is that of presuppositional dependence just in case verifying membership in Q requires reference to A: (24) A set of sets Q presupposes a set A iff for any sufficient condition P for a set X to be in Q, P can only be defined by mentioning A. The semantic anchoring of a domain presupposition is to be achieved in exactly analogous ways to the semantic anchoring of a conceptual presupposition of a proposition: the restriction of the determiner at the index of evaluation must have the same extension as when evaluated with respect to the context of evaluation or else it must be anaphoric to some previously evaluated set description.

21 PRESUPPOSITIONS AND QUANTIFIER DOMAINS 199 Before making this requirement more precise formally, let us turn to the ways the Domain Presupposition manifests itself empirically. The main empirical evidence does not come from the semantics of there-sentences themselves (whose semantics is less obvious), but rather from intensional contexts Weak and Strong Determiners in Intensional Contexts The Domain Presupposition with Universal Quantifiers The crucial observation concerning weak and strong quantifiers in conditionals is found in the contrast between (25a) and (25b) and between (26a) and (26b): (25) a. If John owned every horse (most horses), Mary would be very happy. b. If John owned a horse, Mary would be very happy. (26) a.?? If John owned every unicorn, he would start a zoo. b. If John owned a unicorn, he would start a zoo. Suppose with Lewis (1972) that counterfactual conditionals involve universal quantification over worlds maximally similar to the actual world in which the antecedent is true. The observation then is that in (25a), those worlds must all contain exactly the same horses in their domain as the actual world though those horses will in part be assigned different properties (namely being owned by John). Crucially, the counterfactual worlds cannot differ from the actual one in containing fewer horses (rather than the same horses, but with different properties). That is, the variation permitted by the relation of maximal similarity does not manifest itself in a variation in the domain of a strong quantifier, but only in a variation in the assignment of properties. Domain variation is not excluded by the semantics (or pragmatics) of conditionals per se. In particular, domain-related differences among worlds do not constitute a violation of the condition of maximal similarity. This can be seen, for example, from (25b), where the relevant counterfactual worlds may differ from the actual world in containing an additional horse (standing in the relation of ownership to John). The examples in (26) make the same point. (26a) must involve quantification over actual unicorns, whereas (26b) allows quantification over counterfactual unicorns. The same observation about quantifiers in the antecedent of a counterfactual conditional can be made for quantifiers occurring in the consequent of a conditional:

22 200 F. MOLTMANN (27) a. If John had realized his dreams, he would own every horse. b. If John had realized his dreams, he would own a horse. Every horse in (27a) must range over every actual horse (unless the second, domain-independent reading is invoked). By contrast, a horse in (27b) may easily range also over counterfactual horses. The condition to be fulfilled by the quantifiers in (25a) and (26a) is obviously that the restriction of the determiner be the same when evaluated with respect to the context and with respect to the index. If we use double indexing, then the semantics of counterfactual conditionals can, on the basis of Lewis (1973) semantics, be formulated as follows: (28) [<h!, p,p 0 >] w ¼1 iff for all worlds w 0,w 0 maximally similar to w: if [p] w0 ¼1, then p 0w0 ¼1. Thus, the worlds a counterfactual conditional such as (28a) quantifies over must be such that the horses in that world are the same as in the actual world. Let me then call the condition on strong determiners that their restriction when evaluated with respect to the context be the same as when evaluated with respect to the index the Matching Condition. 13 I will take the Matching Condition to be a condition on the evaluation of strong NPs as generalized quantifiers. Disregarding backgrounds for the moment, the Matching Condition can be formulated as in (29), that is, the restriction of a determiner will have as its content at a context the property whose extension at any index is the same as at the context: (29) The Matching Condition For a domain-presupposing determiner D and a nominal N 0, and world w, [D N 0 ] w ¼[D] w (O), where O is the property such that for any world w 0,O w0 ¼([N 0 ] w ) w. (29) obviously corresponds to the requirement that a presupposed presupposition be true both at the context and the current index. As in the case of the presupposition of propositions, however, (29) need not be fulfilled when the quantifier domain relates to a linguistic antecedent, as in (30a-c): (30) a. If John owned ten horses, he would feed every horse well. b. If John owned ten horses and fed every horse well, Mary would be very happy. c. If John had realized his dreams, he would own ten horses and feed every horse well.